pic comes first, and is this possible to do?In the above graphic, b is the length of one side of the triangle, here defined as the “base”. If you drop a perpendicular from the angle opposite side b to side b, this is called the “height of the triangle”. The area of the triangle, called A, is related to the base and height using the equation: A = (1/2) (base X height) = 0.5bh. In the case where b = 10 cm and h =6 cm, A = 0.5 X 10 X 6 = 30. Kepler’s Three Laws of Elliptical Planetary Motion are written: Planets move in elliptical orbits around the Sun. The line connecting a planet with the Sun, called the Radius Vector, sweeps out equal areas in equal times. The Orbital Period of a planet around the Sun, P, is the time it takes that planet to complete one solar orbit. The square of P is equal is proportional to the planet’s semi-major axis, a. This is expressed using the equation: P2 = Constant a3. If the planet’s orbital period is the years (yr) and the planet’s semi-major axis is in Astronomical Units (au), the Constant in the above equation is equal to 1 and the equation becomes: Pyr2 = aau3. Kepler’s Second Law: Radius Vector Sweeps Out Equal Areas in Equal Times: 2ND pic Table of Data for Kepler’s Second Law Triangle Number Base Length (b) Height Length (h) A = Triangle Area ( bh/2) PE 1 2 3 4 5 6 7 8 ___________________________________________________________________ Average Area (Aav) Please calculate average area by adding together all of the triangle areas and dividing by 8. To calculate Percent Error (PE) for each triangle area, use (A - Aav) PE = 100 ________ , where A is the area of each triangle. Aav Kepler’s Third Law: Pyr2 = aau3. The table below presents the semi-major axis (a) and Actual orbital period for all of the major planet’s in the solar system. Cube for each planet the semi-major axis in Astronomical Units. Then take the square root of this number to get the Calculated orbital period of each planet. Fill in the final row of data for each planet. Table of Data for Kepler’s Third Law: Planet aau = Semi-Major Axis (AU) Actual Planet Calculated Planet Period (Yr) Period (Yr) __________ ______________________ ___________ ________________ Mercury 0.39 0.24 Venus 0.72 0.62 Earth 1.00 1.00 Mars 1.52 1.88 Jupiter 5.20 11.19 Saturn 9.54 29.50 Uranus 19.20 84.00 Neptune 30.10 164.80 __________________________________________________________________ Question 1: Will a comet’s orbit by faster at perihelion or aphelion? Question 2: The semi-major axis of Halley’s Comet is 17.8 AU. How long does it take Halley’s Comet to complete one orbit around the Sun? Here is a scanned version of a reduced centimeter ruler. You may choose to use you own. **Text Explanation:**The average distance of the Earth from the Sun is 150 million kilometers (1.5 x 10^8 km). This is defined as 1 Astronomical Unit or 1 AU. Mercury, the nearest major planet to the Sun, is approximately 0.4 AU from the Sun. Neptune, the farthest known major planet, is about 30 AU from the Sun. All major planets and most asteroids have nearly circular solar orbits, whereas many comets have highly elliptical solar orbits.A key mathematical tool for considering elliptical solar orbits is calculating the area of a triangle.**Diagram Explanation:**- The diagram illustrates a triangle with its base and height labeled. - The "Area of Triangle" is clearly defined with a formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{perpendicular height} \]- The base is shown along the bottom of the triangle, and the perpendicular height is marked with a dotted line reaching from the apex to the base.- This visual helps in understanding how to determine the area of a triangle, which is necessary in calculations involving elliptical solar orbits. **Kepler's 2nd Law Educational Explanation**The graphic above illustrates Kepler’s 2nd Law for a hypothetical comet's elliptical orbit around the Sun. Here's a detailed overview:### Key Points:- **Orbit Numbers:** The elliptical orbit is marked by points 0 through 7. The numbers represents specific positions of the comet over time.- **Time Intervals:** - Points 0 and 1 share the same interval as points 1 and 2. - This pattern continues similarly between consecutive point pairs: 2 and 3, 3 and 4, 4 and 5, 5 and 6, and finally 6 and 7.- **Area Calculation:** - Each pair of points corresponds to an area segment swept by the comet around the Sun. ### Diagram Explanation:- **Description:** The orbit is elliptical, with the Sun positioned along one of its foci (left side of the diagram).- **Triangles and Solar Center:** - **Triangle 1:** Defined by points 0, 3 (on the orbit), and the Sun. - **Triangle 2:** Defined by points 3, 5, and the Sun. - **Triangle 3:** Defined by points 7, 0, and the Sun.- **Calculation Method:** - For each triangle, the base is the line between the Sun and the specified point on the orbit. - You are tasked with determining the height for each triangle. Use the scanned centimeter ruler to accurately measure lengths in centimeters.### Task Instructions:1. **Measure the Sides:** Utilize a centimeter ruler to measure the sides `a` (base) and `b` (height) of each triangle precisely.2. **Calculate the Area:** Once you have the measurements, compute the area for each triangle and record them.This exercise helps you understand Kepler's Law of Areas, emphasizing that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

(1) Aphelion is the point of the Earth's orbit that is farthest away from the Sun. Perihelion is the…

Answered: Question 1: Will a comet’s orbit by…

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pic comes first, and is this possible to do?

In the above graphic, b is the length of one side of the triangle, here defined as the “base”. If you drop a perpendicular from the angle opposite side b to side b, this is called the “height of the triangle”. The area of the triangle, called A, is related to the base and height using the equation:

A = (1/2) (base X height) = 0.5bh.

In the case where b = 10 cm and h =6 cm, A = 0.5 X 10 X 6 = 30.

Kepler’s Three Laws of Elliptical Planetary Motion are written:

Planets move in elliptical orbits around the Sun.

The line connecting a planet with the Sun, called the Radius Vector, sweeps out equal areas in equal times.

The Orbital Period of a planet around the Sun, P, is the time it takes that planet to complete one solar orbit. The square of P is equal is proportional to the planet’s semi-major axis, a. This is expressed using the equation:

P2 = Constant a3.

If the planet’s orbital period is the years (yr) and the planet’s semi-major axis is in

Astronomical Units (au), the Constant in the above equation is equal to 1 and the

equation becomes:

Pyr2 = aau3.

Kepler’s Second Law: Radius Vector Sweeps Out Equal Areas in Equal Times:

2ND pic

Table of Data for Kepler’s Second Law

Triangle Number Base Length (b) Height Length (h) A = Triangle Area ( bh/2) PE

___________________________________________________________________

Average Area (Aav)

Please calculate average area by adding together all of the triangle areas and dividing by 8. To calculate Percent Error (PE) for each triangle area, use

(A - Aav)

PE = 100 ________ , where A is the area of each triangle.

Aav

Kepler’s Third Law: Pyr2 = aau3.

The table below presents the semi-major axis (a) and Actual orbital period for all of the major planet’s in the solar system. Cube for each planet the semi-major axis in Astronomical Units. Then take the square root of this number to get the Calculated orbital period of each planet. Fill in the final row of data for each planet.

Table of Data for Kepler’s Third Law:

Planet aau = Semi-Major Axis (AU) Actual Planet Calculated Planet

Period (Yr) Period (Yr)

__________ ______________________ ___________ ________________

Mercury 0.39 0.24

Venus 0.72 0.62

Earth 1.00 1.00

Mars 1.52 1.88

Jupiter 5.20 11.19

Saturn 9.54 29.50

Uranus 19.20 84.00

Neptune 30.10 164.80